Recall that if the power series f ( x ) = ∑ n = 0 ∞ c n ( x − a ) n {\displaystyle f(x)=\sum _{n=0}^{\infty }c_{n}(x-a)^{n}} has radius of convergence R > 0 , {\displaystyle R>0,} then we can integrate term-wise:
with the resulting series also having a radius of convergence R > 0. {\displaystyle R>0.}
